How does the height from which a table tennis ball is dropped affect its bounce?

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Introduction

How does the height from which a table tennis ball is dropped affect its bounce?

When a table tennis ball is dropped onto a surface it bounces. The height of the bounce depends upon a number of factors; the pressure of the air in the ball, the height from which it is dropped, its material, mass and its temperature; the type of floor surface, its temperature and its angle; and the acceleration due to gravity, the temperature and the air resistance of the air that the ball will pass through. In this experiment I will investigate the way in which the height from which it is dropped affects the bounce of a table tennis ball.

Planning

Objects that fall vertically, without air resistance, all have the same acceleration at ground level on Earth, which is 9.80665m/s2. When the air resistance force on a free-falling object is equal to the pull of gravity, the object will reach its terminal velocity, i.e. it cannot fall any faster. According to Newton’s Second Law, mg - F = ma (in this case, the resultant falling force of the ball minus the air resistance force is equal to the mass of the ball multiplied by its acceleration).

– I think that the height of the table tennis ball’s bounce will always be below the height from which it is dropped due to the loss of energy, predominantly through air resistance (transferred to heat energy due to friction with the air and kinetic energy by moving air out of its way), but also partly through transfer to sound and heat energy on impact with the floor. I think the bounce height will increase with the drop height, but at a slowing rate, i.e. the distance between drop height and bounce height will increase as the drop height increases. I think that once the ball is dropped from a height from which it can accelerate to its terminal velocity, a drop from any height above that will produce the same bounce height, as no further energy will be carried in the ball on impact with the floor.

Analysis

Table of Results

Bounce Height (cm)

Drop Height (cm)

1st drop

2nd drop

3rd drop

20

15

16

15

40

29

30

30

60

42

41

42

80

53

52

54

100

63

61

63

120

75

76

77

140

83

87

85

160

94

91

92

180

98

96

98

200

105

108

105

220

108

109

108

240

112

115

113

260

117

115

118

272

117

118

118

This table shows a complete list of all the results gained in this investigation, all of which are illustrated in the following graph. No bounce height is higher than its drop height, as I stated in my prediction.

Almost every result followed a trend so it is likely that the results as a set were recorded to a satisfactory level of accuracy. However, where there were slightly anomalous results (for example the first drop at 272 centimetres) it is likely that this was due to an abnormality on impact with the floor, such as the ball landing on a slight indentation in the floor or even on a small amount of dirt which might have softened the impact, rather than an error in judgement of the bounce height of the ball. Ideally, and for perfectly accurate results to possibly two decimal places, electronic equipment would still have been used, but I think the correct pattern was still shown using only the human eye. My prediction is likely to be correct in that all the results supported it, though I only had time to vary the concentration over a limited range of values, so I am not sure how true it is outside this range, although the pattern of results suggested that terminal velocity would soon have been reached had more recordings taken place.

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